= Solution
A suitable theorem is the <Baker lower bound for a homogeneous linear form in logarithms>. Let $\alpha_1,\ldots,\alpha_n$ be nonzero algebraic numbers with chosen logarithms and let
$$
\Lambda=b_1\log\alpha_1+\cdots+b_n\log\alpha_n,
\qquad b_i\in\mathbb Z.
$$
Choose $A_i\geq3$ to bound the degree-normalized <Absolute logarithmic Weil height> of $\alpha_i$ and $|\log\alpha_i|$, and put $B=\max(3,|b_1|,\ldots,|b_n|)$. If $\Lambda\ne0$, then
$$
\log|\Lambda|
>-C(\log A_1)\cdots(\log A_n)\log B,
$$
where $C$ is an effectively computable constant depending only on $n$ and the degree of the number field generated by the $\alpha_i$.
Back to article page
